Project Summary The long terms goal of this project is to enable the control of large networks in the brain using neurostimulation technologies, a key focus of the BRAIN initiative. These technologies, including optogenetics, are developing at unprecedented rates and, consequently, are allowing scientists to make increasingly specific extrinsic perturbations to the activity in neural circuits. However, the nature of these perturbations remains largely limited so that the stimulated neuronal population is activated or deactivated en masse. As scientists seek to uncover the finer mechanisms of brain function, methods will be needed that allow more complex spatiotemporal activity patterns ? neural trajectories ? to be induced in these networks. The immense scale and interconnectedness of networks in the brain make this problem highly nontrivial. One may liken this problem to a musician on stage attempting to elicit a specific, unique response from each member of their audience individually, while playing to the group as a whole. To better understand these challenges and attempt to surpass them, our proposal introduces early concepts at the intersection of neuroscience and control theory, the mathematical study of how to optimally ?steer? complex systems subject to their dynamics, possible constraints, and an objective function that measures differences between the desired and induced trajectories. Our specific research aims are grounded in our team's interdisciplinary experience at the interface of dynamical systems, control theory and neuroscience. In Aim 1, we will study how the architecture and dynamics of networks in the brain enable control with respect to natural inputs, i.e., excitation through sensory pathways. In other words, we seek insights into how brain networks control themselves, towards better designing extrinsic stimulation. In Aim 2, we will develop a new toolkit, adapted from modern optimal control engineering, for designing neurostimulation input waveforms that are capable of creating high-dimensional trajectories (e.g., patterns of spikes) in large neuronal networks. In support of Aims 1 and 2, we will develop an innovative benchmark model containing structural and dynamical features pervasive in many salient neuronal networks. Finally, in Aim 3, we will perform in vivo experiments in which we will deploy our theoretical innovations to induce high-dimensional neuronal trajectories in a mouse somatosensory network using optogenetics. The proposed research will yield tangible outcomes in the form of new neurostimulation design methodologies and a benchmark control model that will be disseminated to the broader neuroscience community. Further, our theoretical developments are an important complement to continued growth in stimulation technology and cellular manipulation methods, facilitating a more complete approach to uncovering the mechanisms of the human brain.